The Radon number of the three-dimensional integer lattice

K. Bezdek; A. Blokhuis

doi:10.1007/s00454-003-0003-8

The Radon number of the three-dimensional integer lattice

K. Bezdek, A. Blokhuis

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

In this note we prove that the Radon number of the three-dimensional integer lattice is at most 17, that is, any set of 17 points with integral coordinates in the three-dimensional Euclidean space can be partitioned into two sets such that their convex hulls have an integer point in common.

Original language	English
Pages (from-to)	181-184
Journal	Discrete and Computational Geometry
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s00454-003-0003-8
Publication status	Published - 2003

Bibliographical note

MR2007959 U.S.-Hungarian Workshops on Discrete Geometry and Convexity (Budapest, 1999/Auburn, AL, 2000)

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10.1007/s00454-003-0003-8

Cite this

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title = "The Radon number of the three-dimensional integer lattice",

abstract = "In this note we prove that the Radon number of the three-dimensional integer lattice is at most 17, that is, any set of 17 points with integral coordinates in the three-dimensional Euclidean space can be partitioned into two sets such that their convex hulls have an integer point in common.",

author = "K. Bezdek and A. Blokhuis",

note = "MR2007959 U.S.-Hungarian Workshops on Discrete Geometry and Convexity (Budapest, 1999/Auburn, AL, 2000)",

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T1 - The Radon number of the three-dimensional integer lattice

AU - Bezdek, K.

AU - Blokhuis, A.

N1 - MR2007959 U.S.-Hungarian Workshops on Discrete Geometry and Convexity (Budapest, 1999/Auburn, AL, 2000)

PY - 2003

Y1 - 2003

N2 - In this note we prove that the Radon number of the three-dimensional integer lattice is at most 17, that is, any set of 17 points with integral coordinates in the three-dimensional Euclidean space can be partitioned into two sets such that their convex hulls have an integer point in common.

AB - In this note we prove that the Radon number of the three-dimensional integer lattice is at most 17, that is, any set of 17 points with integral coordinates in the three-dimensional Euclidean space can be partitioned into two sets such that their convex hulls have an integer point in common.

U2 - 10.1007/s00454-003-0003-8

DO - 10.1007/s00454-003-0003-8

M3 - Article

VL - 30

SP - 181

EP - 184

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -

The Radon number of the three-dimensional integer lattice

Abstract

Bibliographical note

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Cite this